Paper Info
Title
Convergence acceleration of Runge-Kutta schemes for solving the Navier-Stokes equations
Abstract
The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7x10^6 and 100x10^6. It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between 4 and 10.
Year
DOI
Venue
2007
10.1016/j.jcp.2007.02.028
J. Comput. Physics
Keywords
DocType
Volume
fourier analysis,damping,aspect ratio,turbulent flow,calculation,preconditioning,stability,runge kutta method,operator,dissipative operator,runge kutta,airfoils,reynolds number,three dimensional,multigrid
Journal
224
Issue
ISSN
Citations 
1
0021-9991
14
PageRank 
References 
Authors
1.39
1
3
Name
Order
Citations
PageRank
Charles Swanson1141.39
Eli Turkel28414.00
Cord-Christian Rossow3233.80